EP3502676A1 - Methode zur bestimmung des wärmeausdehnungskoeffizienten einer kristallinen dünnschicht durch beugung - Google Patents

Methode zur bestimmung des wärmeausdehnungskoeffizienten einer kristallinen dünnschicht durch beugung Download PDF

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Publication number
EP3502676A1
EP3502676A1 EP18214861.9A EP18214861A EP3502676A1 EP 3502676 A1 EP3502676 A1 EP 3502676A1 EP 18214861 A EP18214861 A EP 18214861A EP 3502676 A1 EP3502676 A1 EP 3502676A1
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EP
European Patent Office
Prior art keywords
thin film
thermal expansion
pads
coefficient
diffraction
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EP18214861.9A
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English (en)
French (fr)
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EP3502676B1 (de
Inventor
Patrice Gergaud
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Commissariat a lEnergie Atomique et aux Energies Alternatives CEA
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Commissariat a lEnergie Atomique CEA
Commissariat a lEnergie Atomique et aux Energies Alternatives CEA
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N23/00—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00
    • G01N23/20—Investigating or analysing materials by the use of wave or particle radiation, e.g. X-rays or neutrons, not covered by groups G01N3/00 – G01N17/00, G01N21/00 or G01N22/00 by using diffraction of the radiation by the materials, e.g. for investigating crystal structure; by using scattering of the radiation by the materials, e.g. for investigating non-crystalline materials; by using reflection of the radiation by the materials
    • G01N23/207—Diffractometry using detectors, e.g. using a probe in a central position and one or more displaceable detectors in circumferential positions
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N25/00—Investigating or analyzing materials by the use of thermal means
    • G01N25/16—Investigating or analyzing materials by the use of thermal means by investigating thermal coefficient of expansion
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2223/00—Investigating materials by wave or particle radiation
    • G01N2223/60—Specific applications or type of materials
    • G01N2223/61—Specific applications or type of materials thin films, coatings

Definitions

  • the present invention relates to a method for determining at least one mechanical characteristic of a crystalline thin film deposited on a substrate, for example for determining the coefficient of thermal expansion of the thin film material or the internal residual stress of the film. thin.
  • An implementation method for determining the stresses internal to a thin crystalline film deposited on a substrate or its coefficient of thermal expansion or TEC is to measure its mesh parameter at different temperatures (measurements in situ). This method is for example described in the documents Y. Kuru, M. Wohlschlögel, U. Welzel and EJ Mittemeijer, J. Appl. Cryst. (2008). 41, 428-435 and SP Baker, A. Kretschmann, E. Auto, Acta Mater., 49 (2001), p. 2145 .
  • This method involves measuring a mesh parameter in several directions of space and also requires knowledge of the elastic properties of the film. Indeed, the difference in the coefficient of expansion between the film and the substrate causes stressing of the film when the temperature is varied. The variation of measured mesh parameter due to the variation of temperature is then due, on the one hand, to the natural expansion of the film related to its coefficient of thermal expansion and, on the other hand, to the stress induced by the difference of the thermal coefficients of expansion between the film and the substrate. It is then necessary to separate these two effects.
  • the separation of these effects can be achieved by considering that the variation of mesh parameter due to the coefficient of thermal expansion is isotropic in space, whereas the mechanical stress has an anisotropic effect, that is to say that the variation mesh parameter is different in the plane of the film and according to the normal to the film.
  • the variation of the mesh parameter of the film in different directions of space, for example by rotating the sample, it is possible to separate the effect due to an isotropic deformation and therefore to the coefficient of thermal expansion and the effect deformation anisotropic deformation resulting from differences in coefficients of thermal expansion between the thin film and the substrate.
  • This method of determination therefore requires for several temperatures, measurements in different directions of space. This method is complex and relatively long. In addition, it involves knowing the elastic coefficients of the film and the substrate.
  • a method for determining at least one physical or mechanical characteristic of a crystalline thin film deposited on a substrate comprising the structuring of an area of the thin film in order to cause relaxation at least partial constraint in this area, measuring at least one mesh parameter in this region at several temperatures, and determining at least one mechanical characteristic from these mesh parameter measurements.
  • the inventor has thought to solve the problem of the effect of the difference of thermal expansion coefficients by suppressing this effect, so that this effect does not intervene in the measurements of mesh parameters, instead of isolating it in the measurements made as is the case in the methods of the state of the art.
  • the method according to the invention also makes it possible to determine the stresses internal to the layer, resulting for example from the difference in mesh parameters between the substrate and the thin film and / or deposition conditions.
  • the method also makes it possible to measure the mesh parameters in a portion of the film that has not undergone stress relaxation. By comparing the measured mesh parameter in the relaxed zone and the unrestrained zone, the internal stress in the thin film can be obtained. It is no longer necessary to measure in several directions of space. The duration of implementation of this method is then shorter than that for the methods of the state of the art.
  • the determined physical characteristic may be the coefficient of thermal expansion of the thin film material.
  • an angle detector is used to detect the diffracted beams and in which the detector angularly scans step by step.
  • the determined mechanical characteristic is the internal stress in the thin film.
  • a zone without structuring called “full plate zone” is preserved and said method also comprising the measurement of the mesh parameter of the film outside the network by diffraction at said several given temperatures.
  • the distance between the full plate area and the structured area is sufficient so that the stresses in the full plate area are not relaxed.
  • a position detector is implemented.
  • the grating is for example made by focussed plasma ion beam or by photolithography and etching.
  • the pads have a depth greater than the thickness of the thin film so that the pads comprise a portion of the substrate material.
  • the pads formed comprise inclined flanks.
  • the surface of the array of pads is at least equal to the imprint of the diffraction beam on the thin film.
  • the measurement or measurements of the mesh parameter is preferably carried out by X-ray diffraction or neutron scattering.
  • the present invention also relates to a sample, for the purpose of diffraction analysis, comprising a substrate and a thin film provided with an array of pads whose height is at least equal to the thickness of the thin film, the pads being dimensioning to cause at least partial stress relaxation in this area of the thin film.
  • crystalline is understood to mean a monocrystalline or polycrystalline material.
  • residual stress and “internal stress” are used to denote the stresses in the thin film due to the difference in mesh parameters between the thin film and the substrate and / or the deposition conditions and the difference in coefficients of thermal expansion.
  • FIG. 1 we can see a schematic representation of a sample E having a crystalline thin film 2 which we want to determine one or mechanical characteristics.
  • the sample E also comprises a substrate 4 on one side of which the thin film 2 has been formed.
  • the thin film has a thickness for example of between at least 10 nm and 30 microns.
  • the film has a thickness less than about 5% of that of the substrate.
  • the substrate has for example a thickness of at least a few tens of microns.
  • the thin film is, for example, a material used in microelectronics, for example in metallic, ceramic or semiconductor material, such as silicon, IV-IV, III-V, III-N, II- VI, a metal such as copper, titanium nitride, tungsten
  • the substrate may be of crystalline or amorphous material.
  • the substrate is for example a silicon or sapphire substrate, glass, a metal, a ceramic, etc.
  • the thin film is formed on the substrate, for example by physical vapor deposition, by chemical vapor deposition, by atomic layer deposition or ALD (Atomic Layer Deposition in English terminology).
  • stresses are generated in the thin film, for example due to the difference in the mesh parameter between the material of the thin film and that of the substrate and / or the conditions of formation of the thin film, for example the deposit conditions.
  • an area 6 of the thin film is structured to cause relaxation of the internal stresses of the film in this area.
  • a network of pads 8 is formed in the film.
  • the pads 8 at room temperature are parallelepipedic.
  • the Figure 2B we can see a view from above of the sample including zone 6 of the Figure 2A .
  • the structured area is surrounded by an unstructured area 9 called "full plate area”.
  • the zone has a square shape with a side of dimension c, for example equal to a few tens of microns.
  • the height of the pads 8 is at least equal to the thickness of the thin film 2.
  • the dimensions of the pads in the plane depend on the desired level of relaxation as will be explained below.
  • the structured area is square but a round or other shape may be suitable.
  • the surface of the structured area is chosen to be large enough that, during the diffraction measuring step b), the incident beam can illuminate only the structured area.
  • the surface of the structured zone is preferably chosen to be larger than the imprint of the beam on the surface of the sample, for example the imprint of the beam may be between several ⁇ m 2 and several mm 2 . For example, for a beam of 50 .mu.m in diameter, it is possible to choose a structured square zone of at least 50 .mu.m.
  • the structured area is adjacent to an unstructured, so-called full-plate, i.e. thin film area with unrestrained stresses.
  • the sample comprises a solid plate zone situated at a distance of about at least two times the beam diameter.
  • the distance between the edge of the structured zone and that of the solid plate zone is between a few hundred microns and 1 mm.
  • the pads are also formed in a portion of the thickness of the substrate, which allows a relaxation of constraints more effective.
  • the residual stress of a zone or pad is relaxed when it is negligible compared to the effects of the coefficient of thermal expansion to be determined.
  • the level of relaxation chosen depends on the accuracy of the desired characteristic.
  • the structured zone 6 ' comprises studs 8' formed only in the entire height of the thin layer ( figure 3 ).
  • the array of pads is for example obtained by photolithography and electron beam etching (e-beam in English terminology), or beam-type focused plasma or Plasma-FIB (Plasma Focus Ion Beam in English terminology) .
  • the distance between the pads depends on the process used to produce the structured zone.
  • the blanks 10 of the studs 8 '" are inclined so that their section is trapezoidal, as shown in FIG. figure 3B , even triangular.
  • These forms favor the relaxation of the stresses ie for the same average width of the studs, we obtain a stronger relaxation. Consequently, for the same relaxation, the triangular or trapezoidal shapes may be wider, and therefore require a smaller number of engraving lines. Indeed, as will be explained below, the studs are smaller and the level of relaxation is high.
  • the studs may have a round section in the plane of the sample, the stud may be cylindrical or conical or frustoconical.
  • the level of relaxation is controlled by choosing the shape of the pads, their height, their dimensions in the plane of the film (designated b on the Figure 2B ).
  • the Figure 4A is a graphical representation of the variation of the stress ⁇ in the square-section stubs of side a as a function of the value of a in nm, for several thicknesses of thin film. These variations correspond to pads formed solely in the thin layer (sample of the figure 3A ), ie the height of the pads is equal to the thickness of the thin film. These curves correspond to a thin film-substrate stack of coefficient k equal to 1 or approximately equal to 1, which corresponds to a silicon film on a silicon substrate or Si-Ge film on an Si substrate.
  • the stress is given as a percentage of the nominal stress, i.e. the residual stress of the full plate film. It can be seen that the lower the thickness of the film, the smaller the pads have to relax the stresses.
  • the temperature variation no longer leads to stressing of the film which is relaxed by the edge effects, or leads to negligible stressing compared to the effect of the coefficient of expansion.
  • thermal thin film The variation of the mesh parameter in the engraved area is due to the coefficient of thermal expansion.
  • the measurement of the mesh parameter can be performed in a single direction of space, advantageously the normal to the sample as shown in FIG. Figure 2A .
  • the incident beam is designated I and the reflected beam is Df.
  • a measurement of the mesh parameter is made by diffraction at several temperatures. It can be an X-ray diffraction or a neutron diffraction. In the remainder of the description, we will consider X-ray diffraction.
  • An X-ray diffractometer well known to those skilled in the art is used. It comprises a source S emitting an incident beam I of X-rays and at least one detector D of the diffracted beam Df ( Figure 2A ).
  • the sample is available on or in temperature control means. It can be an oven or a cryostat. Indeed, the measurements can be made at low temperature, for example at the temperature of liquid nitrogen or liquid helium.
  • the measurement direction is normal to the plane of the sample, the angle of incidence of the beam relative to the surface is then equal to the diffraction angle with respect to the surface.
  • the measurement is made for a crystalline plane hkl.
  • the interplanar distance measured for this plane is a combination of the lattice parameters of the crystal structure.
  • the coefficient of thermal expansion measured for this plane is therefore a combination of the coefficients of thermal expansion of these different mesh parameters. If one wishes to extract the coefficient of thermal expansion of each parameter, one measures from 1 to 6 independent hkl planes according to the crystalline symmetry. For a cubic crystal only one measure is enough, for a tetragonal crystal (a, b, c), 3 planes are necessary, etc ...
  • the measurements are made at different temperatures. Preferably, sufficient measurements are made to achieve linear regression, especially if it is assumed that the coefficient of thermal expansion depends on the temperature. If the coefficient of thermal expansion does not depend on the temperature, two measurements may suffice, one for example at room temperature and the other at a temperature which may be the minimum or maximum temperature considered.
  • the value of the mesh parameter d varies depending on the temperature due to the coefficient of thermal expansion only or at least mainly.
  • the determination of the coefficient of thermal expansion is fast and very simple and implements very few calculations in comparison with the methods of the state of the art. Moreover, it does not require measurement in the different directions. Thanks to the method according to the invention, there is a quasi-direct measurement of the coefficient of thermal expansion, since the calculations to obtain it from the measurements of the mesh parameter are simple and fast and do not require to take into account special conditions relating to films.
  • the determination of the X-ray diffraction mesh parameters is well known to those skilled in the art and will not be described in detail. Thanks to the X-ray diffraction, one obtains the intensities of the reflections, their positions and their line widths. From the positions of the reflections in the three-dimensional space, the mesh parameter (s) and the Bravais array of the crystal are determined; the crystal mesh parameters in the direct network are calculated from those of the reciprocal lattice measured by diffraction (Fourier transform of the direct network). It is from the direct network that the coefficient of thermal expansion can be determined.
  • the coefficient of thermal expansion is calculated using equation 1.
  • the variation of the mesh parameter d is plotted as a function of temperature. Calculation of the derivative of this curve gives the coefficient of thermal expansion at each temperature. If the coefficient of thermal expansion is independent of the temperature, the relation function is linear, otherwise the thermal expansion coefficient for each temperature is determined.
  • the furnace undergoes expansion, which can cause a displacement of the sample and therefore of the structured area targeted by the incident beam, along the normal to the plane of the sample.
  • the diffraction peaks are angularly offset, but it is the precise location of the diffraction peaks that makes it possible to measure the mesh parameters.
  • a diffracted beam angle detector i.e. a detector having angular selectivity, which is capable of determining the angle of the beam diffracted directly from its direction.
  • This type of sensor is also referred to as a 0D detector and is provided with an angularly selective slit set. The angle of the diffracted beam is measured by angularly scanning the detector.
  • the displacement of the sample along the normal to the plane of the sample is then dispensed with.
  • a crystal analyzer can be used to perform the same function as the set of selective slots. According to another variant, it is possible to calibrate previously the furnace in displacement with the temperature and make a correction of the position of the oven a priori or a correction of diffraction angles a posteriori.
  • the method according to the invention makes it possible to more simply determine the coefficient of thermal expansion of a crystalline thin layer in comparison with the methods of the state of the art.
  • the method according to the invention makes it possible to determine the internal or residual stress of the thin film.
  • the sample comprises a solid plate zone 9 sufficiently far away from the structured zone 6 so that it is not sensitive to the relaxation of the stresses in the structured zone, so the stress in the solid plate zone is the stress of the film without structured area ( figure 6 ).
  • the arrows I1, I2 and Df1, Df2 denote the respectively incident and diffracted beams on the structured zone and on the full plate zone.
  • the measurement in the structured zone gives the unconstrained mesh parameter and the measurement in the full plate zone gives the constrained mesh parameter, one can then directly determine the deformation and thus the stress of the thin film.
  • the diffracted ray detection is done with a position detector, designated a 1D detector, which may be a CMOS or wire detector.
  • the determination of the stress is substantially faster than with the methods of the state of the art, of the order of 10 to 100 times faster.
  • a detector 0D for example a scintillator or a proportional detector.
  • the measurement time is longer than with a 1D detector.
  • the determination of the coefficient of thermal expansion and the determination of the stress can advantageously be simultaneous, since in both determinations the measurement of the mesh parameter in the structured zone takes place.
  • the method for determining the thermal expansion coefficient of the thin film and the method for determining the stress in the thin film are simplified.

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EP18214861.9A 2017-12-22 2018-12-20 Methode zur bestimmung des wärmeausdehnungskoeffizienten einer kristallinen dünnschicht durch beugung Active EP3502676B1 (de)

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FR1763168A FR3075963B1 (fr) 2017-12-22 2017-12-22 Methode de determination d'au moins une caracteristique physique ou mecanique d'un film mince cristallin par diffraction

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EP3502676A1 true EP3502676A1 (de) 2019-06-26
EP3502676B1 EP3502676B1 (de) 2022-05-25

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112986320A (zh) * 2021-02-07 2021-06-18 复旦大学 一种薄膜热膨胀系数的测定方法

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
BAKER: "Thermomechanical Behavior of different texture components in Cu thin films", 1 January 2001 (2001-01-01), pages 2145 - 2160, XP055508053, Retrieved from the Internet <URL:https://www.sciencedirect.com/science/article/pii/S1359645401001276/pdfft?md5=1377add9718373d2bd8f67150228b54f&pid=1-s2.0-S1359645401001276-main.pdf> [retrieved on 20180919] *
JOZEF KECKES: "Simultaneous determination of experimental elastic and thermal strains in thin films", JOURNAL OF APPLIED CRYSTALLOGRAPHY., vol. 38, no. 2, 11 March 2005 (2005-03-11), DK, pages 311 - 318, XP055507988, ISSN: 0021-8898, DOI: 10.1107/S0021889805001044 *
NIKOLAOS BAIMPAS ET AL: "Stress evaluation in thin films: Micro-focus synchrotron X-ray diffraction combined with focused ion beam patterning for do evaluation", THIN SOLID FILMS, vol. 549, 1 December 2013 (2013-12-01), AMSTERDAM, NL, pages 245 - 250, XP055507216, ISSN: 0040-6090, DOI: 10.1016/j.tsf.2013.07.019 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112986320A (zh) * 2021-02-07 2021-06-18 复旦大学 一种薄膜热膨胀系数的测定方法

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FR3075963A1 (fr) 2019-06-28
EP3502676B1 (de) 2022-05-25

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